1. Field of the Invention
The present invention is in the field of telecommunications and, in particular, in the field of multi-carrier transmission techniques.
2. Description of Related Art
Multi-carrier transmission is a promising modulation scheme for e.g. 4th generation mobile communication systems (4G) because it allows to transmit over a broad bandwidth and to achieve high-speed and large capacity throughput performance. One of the problems associated with multi-carrier modulation schemes is an increased peak-to-average power ratio (PAPR) resulting from a super-position of a plurality of frequency signal components in a time domain signal to be transmitted. The problem associated with high signal peaks in a multi-carrier modulation technique results from the fact that a high PAPR causes clipping or bad resolution in digital-to-analogue converters and non-linear distortion in high power amplifiers (HPA), which causes serious out-of-band emissions disturbing adjacent signals. Generally, high PAPR makes a signal detection at a receiver difficult and, therefore, leads to an increased bit error rate.
Among other multi-carrier transmission techniques, the orthogonal frequency division multiplexing (OFDM) is frequently used. At a transmitter, an OFDM signal is obtained from assigning a number of spectral values to be transmitted to subcarriers used for transmission, wherein a transmit signal is obtained from an inverse Fourier transform applied to the spectral values. The spectral values are obtained from dividing information values into groups containing a number of information values and mapping the groups of information values onto signal space constellation points in a signal space domain. Therefore, a group of information values is represented by a signal space constellation point having a real part and an imaginary part. The mapping operation is equivalent to modulating the groups of information bits using a modulation technique, for example, a quadrature amplitude modulation (QAM), assigning a group of information values to a signal space constellation point from a set of signal space constellation points associated with the modulation technique.
In the case of OFDM, high signal peaks origin from superposing the subcarriers. The high power amplifier heavily distorts all signal parts that come close to, or exceed saturation. The distortion causes inter-carrier interference (ICI) and the above-mentioned OOB radiation. While ICI disturbs the transmitted signal and degrades the bit error rate (BER), OOB radiation disturbs signals on adjacent frequency bands and should also be avoided.
Known peak reduction techniques are used in order to mitigate the negative effects of nonlinear distortion. Non-distortion techniques like selective mapping (SLM), partial transmit sequences (PTS) and derivatives can achieve a good peak reduction by transmitting only symbols with low peaks. The SLM approach is disclosed in S. H. Müller, R. W. Bäuml, R. F. H. Fischer and J. B. Huber, “OFDM with Reduced Peak-to-Average Power Ratio by Multiple Signal Representation,” Annals of Telecommunications, Vol. 52, No. 1-2, pp. 1-9, February, 1997, the PTS approach is disclosed in S. H. Müller and J. B. Huber, “A Comparison of Peak Power Reduction schemes for OFDM,” in Proc. Of Globecom. November 1997, pp. 1-5.
A transmission of side information is one problem associated with non-distortion techniques, so that a data structure has to be changed. Known non-distortion techniques require extensive effort at the transmitter in order to find the symbol with the lowest peaks and require additional efforts at every receiver in order to restore the signal.
In order to reduce PAPR, coding techniques, as disclosed in A. E. Jones, T. A. Wilkinson and S. K. Barton, “Block Coding Scheme for Reduction of Peak to Mean Envelope Power Ratio of Multicarrier Transmission Schemes,” El. Lett, Vol. 30, No. 25, pp. 2098-2099, December 1994 can be used. Coding techniques use codes, whose codewords have low PAPR. This, however, generally limits the flexibility in transmitter design. Furthermore, if channel codes are designed for low PAPR, same cannot be used anymore in order to optimise system performance by fitting the code for the channel and the transmission scheme. Moreover, for a high number of subcarriers in a case of a multi-carrier transmission technique like OFDM, the code rate of the currently known peak reduction codes must be low in order to achieve a significant PAPR reduction.
Using peak reduction carriers/tones (PRC/PRT) disclosed in E. Lawrey and C. J. Kikkert, “Peak to Average Power Ration Reduction of OFDM Signals Using Peak Reduction Carriers,” in Int. Symposium on signal Processing and its applications, August 1999, pp. 737-740, J. Tellado and J. M. Cioffi, “Peak Power Reduction for Multicarrier Transmission,” in Mini-Globecom, 1999, optionally in combination with adaptive subcarrier selection (ASuS) disclosed in H. Schmidt and K.-D. Kammeyer, “Reducing the Peak to Average Power Ratio of Multicarrier Signals by Adaptive Subcarrier Selection,” in Int. Conference on Universal Personal Communications, January 1998, pp. 933-937, offers some degrees of freedom to reduce PAPR without introducing ICI on the data carriers. However, for a strong reduction of PAPR, many peak reduction carriers are needed corresponding to a significant loss in data rate. ASuS is using only the weakest subcarriers for peak reduction and therefore requires feedback information from the receiver about the channel state information (CSI). However, the more receivers have to be reached, the less probable it becomes to find subcarriers that are weak for all receivers.
Clipping techniques offer a high flexibility, as many of them are basically applicable for any modulation scheme. Whereas clipping and filtering in time domain, as is disclosed in L. D. Kabulepa, T. Pionteck, A. Garcis and M. Glesner, “Design Space Exploration for Clipping and Filtering PAPR Reduction Techniques in OFDM Systems,” in Proc. Int. OFDM-Workshop, Vol. 1, October 2003, pp. 108-112, offers a peak reduction at low implementation costs, repeated clipping and frequency filtering disclosed in J. Armstrong, “Peak-to-Average power reduction for OFDM by repeated clipping and frequency domain filtering,” in E1. Lett. Vol. 38, No. 5, February 2003, pp. 246-247 allows to remove that part of the out-of-band radiation completely that is introduced by clipping. However, most clipping techniques introduce ICI. This undesirable effect becomes significant when the clipping ratio is chosen low in order to achieve a low out-of-band radiation.
The filtering operation and the peak regrowth that is incorporated with the filtering can be avoided when soft clipping, as disclosed in H.-G. Ryu, B.-I Jin and I.-B. Kim, “PAPR Reduction Using Soft Clipping and ACI Rejection in OFDM Systems,” IEEE Trans. On Communications, Vol. 48, No. 1, pp. 17-22, February 2002, peak windowing as disclosed in M. Pauli and H.-P. Kuchenbecker, “On the Reduction of the Out-of-Band Radiation of OFDM-Signals,” in Int. Conference on Communications, Vol. 3, 1998, pp. 1304-1308 or peak cancellation techniques as disclosed in M. Lampe and H. Rohling, “Reducing out-of-band emissions due to nonlinearities in OFDM systems,” in Vehicular Technology Conference, Vol. 3, May 1999, pp. 2255-2259 are used. However, this is done at the expense of additional ICI.
Improving the ICI can be done at the transmitter by predistorting the signal as is disclosed in A. Katz, “Linearization: Reducing Distortion in Power Amplifiers,” IEEE Microwave Magazine, Vol. 2, No. 4, pp. 37-49, December 2001. This compensates for the amplifier's nonlinearity. However, signal peaks exceeding the amplifier's saturation are still distorted, so that supplementary peak reduction techniques have to be used. Complementarily, it is possible to model the distorted transmitted signal and to consider the limited dynamic range by a Bayesian estimator at the receiver as is disclosed in P. Zillmann, H. Nuszkowski and G. P. Fettweis, “A Novel Receive Algorithm for Clipped OFDM Signals,” in Proc. Int. Symp. On Wireless Personal Multimedia Communications, Vol. 3, October 2003, pp. 385-389.
As one further possibility companding techniques as disclosed in X, Wang, T. T. Tjhung and C. S. Ng, “Reduction of Peak-to-Average Power Ratio of OFDM System Using a Companding Technique,” IEEE Trans. On Broadcasting, Vol. 45, No. 3, pp. 303-307, September 1999 can be used. They are composed of a transmit processing part that compresses the signal at the transmitter and a receive processing part that expands the signal to the original dynamic range with low complexity. Alternative techniques that have a deeper impact in the receiver's design are decision-aided reconstruction (DAR) as disclosed in D. Kim and G. L. Stuber, “Clipping Noise Mitigation for OFDM by Decision-Aided Reconstruction,” IEEE Communications Letters, Vol. 3, No. 1, pp. 4-6, January 1999 or iterative maximum likelihood detection as disclosed in J. Tellado, L. M. C. Hoo and J. M. Cioffi, “Maximum-Likelihood Detection of Nonlinearly Distorted Multicarrier Symbols by Iterative Decoding,” IEEE Trans. On Communications, Vol. 51, No. 2, pp. 218-228, February 2003. They require, however, significantly more computational complexity at the receiver.
The active constellation extension (ACE) technique disclosed in B. S. Krongold and D. L. Jones, “PAR reduction in OFDM via Active Constellation Extension,” IEEE Trans. On Broadcasting, vol. 49, No. 3, pp. 258-268, September 2003 considers the ICI without any modifications at the receiver. The outer constellation points in the signal space (signal space domain) are extended to minimize the PAPR. After clipping the signal peaks, undesired extension directions in the signal space are set to zero so that the decision boarders are never approached. However, it is not possible to achieve very low OOB radiation and it is effective mainly for small constellation sizes, e.g. for quaternary phase shift keying (QPSK).
The tone injection technique disclosed in J. Tellado and J. M. Cioffi, “Peak Power Reduction for Multicarrier Transmission,” in Mini-Globecom, 1999, which belongs to a class of non-distortion techniques, is an alternative to ACE that also extends the signal constellation, but it is more suitable for higher-order constellations. The tone injection results in a higher order signal constellation, e.g. a 16 QAM amplitude modulation symbol may be transformed to a 144 QAM symbol. This avoids ICI, but the average symbol energy increases and so does the required signal-to-noise ratio (SNR).
In the following, OFDM modulation for transmitting on multiple subcarriers, serving as an example of a multi-carrier modulation scheme, will be considered by the way of example only. dn(i) are the complex data symbols transmitted at time instant i on subcarrier n. The transmitted signal after OFDM modulation
      s    ⁡          (      t      )        =            ∑              i        =                  -          ∞                    ∞        ⁢                  ∑                  n          =          0                          N          -          1                    ⁢                                    d            n                    ⁡                      (            i            )                          ⁢                              g            n                    ⁡                      (                          t              -              iT                        )                              is composed of the N subcarriers dn(i), wheregn(t)=g(t)ejwntare the transmit filters. For example, raised cosine impulse shapes can be selected for g(t).
For example, the HPA may be represented by Rapp's solid state power amplifier (SSPA) model disclosed in H. Atarashi and M. Nakagawa, “A Computational Cost Reduction scheme for a Post-Distortion Type Nonlinear Distortion Compensator of OFDM Signals,” IEICE Trans. On communications, vol. E81-B, No. 12, pp. 2334-2342, December 1998 with amplification characteristic
            s      _        ⁡          (      t      )        =            Vs      ⁡              (        t        )                            (                  1          +                                                                                    Vs                  ⁡                                      (                    t                    )                                                  /                                  A                  SAT                                                                                  2              ⁢              p                                      )                              1          /          2                ⁢        p            where p=10, s(t) is the amplified signal, V can be considered as being an amplification factor, andPSAT=ASAT2is the amplifiers saturation power.
In order to reduce the nonlinear distortion of peaks, the amplifier is driven with an output back-off (OBO). The OBO is defined as the ratio between the amplifier's saturation power and the power of the amplifier's output signal
      OBO    ⁢          |      dB        ⁢      =    △    ⁢      10    ⁢          log      10        ⁢                  P        SAT                    E        ⁢                  {                                                                                    s                  _                                ⁡                                  (                  t                  )                                                                    2                    }                    
Without any further measures, the OFDM signal may exceed the amplifiers saturation from time to time. In order to reduce the dynamic range of the OFDM signal s(t) clipping techniques can be used to cut peak amplitudes.
FIG. 12 shows a block diagram of an OFDM transmitter incorporating the clipping approach in order to reduce PAPR.
The transmitter in FIG. 12 demonstrates non-recursive clipping (solid lines), as disclosed in J. Armstrong, “New OFDM Peak-to-Average Power Reduction Scheme,” in Vehicular Technology Conference, Vol. 1, Spring 2001, pp. 756-760. Moreover, the transmitter shows the recursive clipping approach depicted with dashed lines.
The transmitter shown in FIG. 12 comprises a data symbol source 1500 having an output coupled to an input of a zero padding block 1501. The zero padding block 1501 is coupled to an inverse fast Fourier transformer (IFFT) 1503. An output of the IFFT is coupled to a clipping block 1505 having an output coupled to a fast Fourier transformer (FFT) 1507. An output of the FFT 1507 is coupled to a filter 1509, the filter 1509 having an output coupled to an OFDM modulator 1511.
Using a recursive clipping technique, a filtered signal provided by the filter 1509 is fed back to the zero padding block 1501.
The data symbols on subcarriers
      d    0    ⁢      =    △    ⁢            (                        d          0                ,        …        ⁢                                  ,                  d                      N            -            1                              )        T  are first transferred into a time domain signal using the IFFT block 1503. The zero padding before the FFT leads to an oversampling in time domain. Next, the signal is clipped at a clipping level xmax. A clipping ratio CR is defined by
      CR    ⁢          |      dB        ⁢      =    △    ⁢      10    ⁢          log      10        ⁢                  x        max        2                    E        ⁢                  {                                    d                              0                ⁢                H                                      ⁢                          d              0                                }                    
The clipped signal is transformed back into the frequency domain. While the first N elements of the FFT output are the new data symbols that correspond to the amplitude limited time signal, the other part of the output vector contains only intermodulation products that would appear as OOB radiation on the channel. These elements are suppressed by the filtering block 1509 of the system.
The disadvantage of clipping is the error between the original data symbols and the new data vector. This difference is the ICI which has previously been mentioned.
Contrary to the clipping and symbol-by-symbol filtering approach described above, a repeated clipping and frequency domain filtering associated with the recursive clipping is depicted with the dashed lines in FIG. 12. While the clipped signals amplitude is peak reduced, the filtering removes all high frequencies and the peaks regrow. For this reason, it may be of advantage to repeat clipping and filtering. Therefore, the filtered signal is fed back, as is shown in the dashed part of FIG. 12. Although any number of iterations is possible, it has been shown in A. Saul, “Analysis of Peak Reduction in OFDM Systems Based on Recursive Clipping,” in Proc. Int. OFDM-Workshop, Vol. 1, September 2003, pp. 103-107 that depending on the system parameters, at most one repetition of clipping and filtering may be of advantage in many cases.
An alternative technique to that described above is the ACE technique previously mentioned. The basic concept behind the ACE technique can be summarised as extending the constellation points in the symbol space (signal space domain) while applying a set of constraints. The constraints prevent symbols to approach the decision boarders in the complex signal space.
FIG. 13 shows a block diagram of a transmitter using the ACE technique.
The ACE transmitter comprises the data symbol source 1500 coupled to an IFFT 1600 having an output 1601. The IFFT 1600 performs an inverse Fourier transform and oversampling and has the same function as the blocks zero-padding 1501 and IFFT 1503 in FIG. 12. The output 1601 is coupled via a switch 1603 to a subtractor 1605, to a clipping block 1607, to an ACE constraint block 1609, to an SGP block 1611 (SGP=smart gradient project) and to the adder 1613.
An output of the subtractor 1605 is coupled to an FFT 1615 having an output coupled to the ACE constraint block 1609. The FFT 1615 performs a Fourier transform and filtering, which is comparable to the operation of the blocks 1507 and 1509 in FIG. 12. The ACE constraint block 1609 has an output coupled to an IFFT 1617 having an output coupled to a multiplier 1619. The IFFT 1617 performs an inverse Fourier transform and oversampling. The multiplier 1619 has a further input to which an output of the SGP 1611 is coupled. The SGP 1611 has a further input to which the output of the IFFT is coupled. An output of the multiplier 1619 is coupled to an input of the adder 1613. An output of the adder 1613 is coupled via a switch 1621 to an impulse-shaping block 1623.
The ACE transmitter shown in FIG. 13 further comprises a feedback loop 1625 connecting the output of the adder 1613 with the input of the subtractor 1615, when the switches 1603 and 1621 are appropriately switched.
Similar to the other clipping techniques described above, the oversampled time signal provided by the IFFT 1600 is clipped by the clipping block 1607. In order to allow only certain extension directions, the clipped signal portion is transformed into the frequency domain using the FFT 1615, where unwanted extension directions are set to zero in the ACE constraint block 1609. After transforming back into time domain, the μ-fault of the extension vector provided by the IFFT 1617 is added to the original unclipped signal.
The weighting factor μ is determined by the above-mentioned smart gradient project algorithm in a sub-optimum, but computational efficient way, so that a peak reduction can be achieved. In order to reduce peaks further, the procedure can be repeated several times. In practice, one or two repetitions seem to be reasonable.
FIG. 14a shows a signal space constellation after recursive clipping at CR=3.1 dB. Recursive clipping superposes an approximately white Gaussian-noise like signal to the subcarriers and ACE shapes the interference so that no signal points are close to the decision boarders. FIG. 14b illustrates the signal space constellation after ACE for a QPSK signal with CR=5.0 dB. As is depicted in FIG. 14b, non-acceptable extension directions will be set to zero. The extension direction is non-acceptable, if the signal point would approach the decision boarders. In reference to FIG. 4a, sub-carriers in the top corner fully contribute to peak reduction. Sub-carriers in the top left corner only contribute with imaginary part, since the real part of the extension vector will be set to zero. Sub-carriers in the bottom right corner only contribute with real part, since the imaginary part of the extension vector will be set to zero.
If, for example, a clipping level is too low, then only a few of signal points remain within the right-angled area, so that only few signal points contribute to PAPR reduction. However, the fewer signal points remain within the allowed area, the more insufficient PAPR reduction can be achieved. Although an increased clipping level would introduce more signal points within the allowable area, the OOB radiation would increase in this case, so that other transmitters on adjacent frequency bands are disturbed.